Faster Approximation To Multivariate Functions by Combined Bernstein-Taylor Operators

Abstract

In this article, we incorporate multivariate Taylor polynomials into the definition of the Bernstein operators to get a faster approximation to multivariate functions by these combined operators. We also give various numerical simulations including graphical illustrations and error estimations. Our results improve not only the linear approximation by classical Bernstein polynomials but also the nonlinear approximation obtained by max-product operations. © 2025 the author(s), published by De Gruyter.